Source: https://guthlabs.ai/docs/instruments/fin-effectiveness-efficiency-calculator/
instrument / verified-clean
# Fin Effectiveness/Efficiency Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Thermodynamics, Fluids & Aero
**Tranche**: tranche-4
**Evidence ID**: t4-156
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The m, corrected-length efficiency, and corrected-length heat-rate calculations are standard under the stated assumptions, and the numerical vectors verify them. The instrument cannot receive a PASS because effectiveness is claimed but undefined, and the specification does not unambiguously distinguish exact adiabatic-tip formulas from corrected-length approximations or define L_c.
### Formula and scope findings
- The effectiveness formula is missing, so the claimed effectiveness output cannot be computed or verified. A standard definition is ε_fin=q_fin/(h A_b θ_b), but the reference base area A_b is not specified.
- The formula η_fin=tanh(mL_c)/(mL_c) is the corrected-length approximation, not the exact adiabatic-tip expression unless L_c is explicitly defined as L+A_c/P.
- The heat-rate expression using tanh(mL_c) is likewise a corrected-length approximation. For an exact adiabatic-tip model it should use tanh(mL), with the corresponding fin-area convention for efficiency.
- The geometry-to-parameter definitions are absent: rectangular and pin-fin formulas for A_c and P must be specified, as must whether L is physical fin length or corrected length.
- The limiting case mL_c=0 is not defined; efficiency should use the limit η_fin=1 rather than direct division by zero.
### Unit assumptions
- Use SI units consistently: h in W/(m²·K), k in W/(m·K), lengths in m, A_c in m², P in m, and θ_b in K or °C temperature difference.
- m has units of 1/m, so mL_c is dimensionless.
- For these vectors, L_c is assumed to mean L+A_c/P, the standard corrected-length approximation for a convecting fin tip.
- Temperature differences in kelvins and degrees Celsius are numerically interchangeable.
- The heat-rate output q_fin is in watts.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The raw formulas expose undefined behavior for k = 0, and the zero-length limiting case produces a 0/0 effectiveness unless the calculator explicitly applies the limiting value or rejects the effectiveness output.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"geometry": "rectangular",
"t_m": 0.002,
"w_m": 0.048,
"L_m": 0.04904,
"k_W_per_mK": 200,
"h_W_per_m2K": 19.2,
"theta_b_K": 80,
"A_c_m2": 0.000096,
"P_m": 0.1,
"L_c_m": 0.05
},
"expected_outputs": {
"m_per_m": 10,
"eta_fin": 0.92423431,
"q_fin_W": 7.09811954
},
"working": "A_c=t·w=0.002·0.048=0.000096 m²; P=2(t+w)=2(0.002+0.048)=0.1 m; L_c=L+A_c/P=0.04904+0.000096/0.1=0.05 m; m=√(hP/(kA_c))=√(19.2·0.1/(200·0.000096))=√100=10 m⁻¹; mL_c=10·0.05=0.5; tanh(0.5)=0.46211716; η_fin=0.46211716/0.5=0.92423431; √(hPkA_c)=√(19.2·0.1·200·0.000096)=√0.036864=0.192; q_fin=0.192·80·0.46211716=7.09811954 W."
}
````
## Related workflows
[Heat-Transfer Pathextended surfaces]()
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`